We introduce the Kodaira dimension of contact 3-manifolds and show that contact 3-manifolds with distinct Kodaria dimensions behave differently when it comes to the geography of various kinds of fillings. We also prove that, given any contact 3-manifold, there is a lower bound of $2\ chi+ 3\ sigma $ for all its minimal symplectic fillings. This generalizes the similar bound of Stipsicz for Stein fillings. This talk is based on joint works with Cheuk Yu Mak, and partly with Koichi Yasui.